{
  "id": "2212.01652",
  "version": "v1",
  "published": "2022-12-03T17:03:49.000Z",
  "updated": "2022-12-03T17:03:49.000Z",
  "title": "Tangent groupoid and tangent cones in sub-Riemannian geometry",
  "authors": [
    "Omar Mohsen"
  ],
  "categories": [
    "math.DG",
    "math.MG",
    "math.OA"
  ],
  "abstract": "Let $X_1,\\cdots,X_m$ be vector fields satisfying H\\\"ormander's Lie bracket generating condition on a smooth manifold $M$. We generalise Connes's tangent groupoid, by constructing a completion of the space $M\\times M\\times \\mathbb{R}_+^\\times$ using the sub-Riemannian metric. We use our space to calculate all the tangent cones of the sub-Riemannian metric in the sense of the Gromov-Hausdorff distance. This generalises a result of Bella\\\"iche.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-03T17:03:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tangent cones",
      "sub-riemannian geometry",
      "generalise conness tangent groupoid",
      "sub-riemannian metric",
      "lie bracket generating condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}